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There Is a Dollar Amount Where Campaign Spending Stops Helping and Starts Hurting Democracy
In A Nutshell
- A physics-based model calibrated to 40 years of U.S. House races finds that once both campaigns exceed roughly $1.83 million in spending, local social influence on voters diminishes sharply and close races tend to end near a 50-50 split.
- Past that threshold, additional spending makes little difference in the model: the race is effectively locked by partisan alignment rather than persuasion.
- Incumbents hold a built-in structural advantage below the threshold, but challengers still need to spend roughly $140,000 even against an opponent who spends nothing.
- Races crossing the $1.83 million threshold on both sides jumped sharply in 2018 and 2020, a trend the researchers link to rising political polarization, though they caution it requires further validation.
American voters like to think their neighbors can change their minds. A conversation at the barbershop, a lawn sign, or perhaps a family dinner can potentially shift a perspective. But a new study out of Austria suggests that once both campaigns in a U.S. House race cross roughly $1.8 million in spending, local social influence matters far less, and campaign alignment begins to dominate. In already close districts, results tend to cluster near an even split, with extra spending past that point making little difference in the model.
Researchers at the Complexity Science Hub in Vienna published their findings in Physical Review Letters, applying a framework from physics, the same math used to model how atoms align in magnets, to four decades of congressional elections. Political polarization, they found, is not just a cultural mood. It behaves like a phase transition, the kind of abrupt change that turns water into ice. Cross a certain campaign spending threshold, and the entire character of a race flips. In the model, more money past that point does not keep buying votes. It helps lock in a standoff.
Two forces compete for every voter’s attention, according to the model. One is homophily, the tendency to spend time with and be shaped by people who think like us, whether friends, family, or coworkers. The other is campaign messaging, which most voters follow almost exclusively from their own party’s outreach. When spending is low, the model suggests local social influence has more room to matter, and outcomes are more likely to reflect district-level conditions and voter relationships. When both campaigns climb past a critical spending level, that influence fades. In already close districts, partisan alignment takes over, and the race heads toward a dead heat.
Campaign Spending Polarization Hits a Tipping Point at $1.83 Million
To find that tipping point, the researchers combed through 6,357 U.S. House races from 1980 to 2020, pulling campaign finance data from the Federal Election Commission and a Stanford University database. Only head-to-head Democratic versus Republican contests were included, with all spending figures adjusted to 2020 dollars. Rather than looking for who spent more, they looked for the spending level at which the model predicts district-level social dynamics stop driving outcomes.
That number landed at approximately $1.83 million per campaign. Below it, elections tend to be decisive, shaped by local conditions and voter relationships. In close contests where both campaigns spent nearly the same amount and exceeded the threshold, more than 70 percent of races ended near a 50-50 split. At that point, additional dollars made no meaningful difference in the model.
Challengers Face a $140,000 Barrier Even When Incumbents Spend Nothing
Beyond the spending threshold, the model also puts hard numbers on something strategists have long sensed: incumbents hold a structural edge that exists regardless of campaign activity. Below the critical spending level, the researchers identified a zone, one where prior election history rather than current spending determines the outcome, in which sitting officeholders tend to win even when outspent. A challenger must spend roughly $140,000 just to be competitive against an incumbent who spends nothing at all. When that incumbent spends roughly $915,000, about half the critical threshold, the challenger’s disadvantage still amounts to about 20 percent of total campaign cost.
Once both campaigns cross $1.83 million, that cushion can shrink. In close districts, races tighten toward near-even splits, and the local social dynamics that once shaped outcomes recede further. High spending does not simply amplify the partisan divide. It displaces much of what was there before.
Campaign Spending Polarization Spiked Sharply in 2018 and 2020
Looking across four decades of data, the share of House races where both campaigns exceeded the $1.83 million threshold stayed relatively low through most of the period. Then came 2018 and 2020, when that share jumped sharply. “Campaigns exceeding critical expenditures increased in 2018 and 2020, suggesting a boost in political polarization,” the authors write, though they caution the trend rests on model predictions and needs further validation. A related study cited by the authors also found rising polarization in Congress after the Supreme Court’s 2010 approval of Super PACs, which dramatically expanded the flow of outside money into races.
Caps on Campaign Spending May Be the Only Check on Structural Polarization
Campaign finance debates usually center on corruption or donor influence. This research reframes the stakes. When both sides spend past the tipping point, the researchers argue, it is not just one race that suffers. It is what the model treats as the district’s social fabric: the conversations and relationships that may give local conditions their influence on outcomes.
As the authors note, “polarization erodes ties across divides and exacerbates fragmentation,” and they suggest that caps on campaign spending “may be needed to prevent undesirable outcomes.” Forty years of election data, filtered through equations built for magnets, point to a dollar figure where the damage starts. Whether that number ever informs policy is an open question, but the researchers argue that unchecked campaign intensity may carry broader social costs.
Paper Notes
Limitations
The model relies on a mean-field approximation and assumes voters follow only one party’s campaign, simplifying real-world behavior. The analysis covers only two-party races, excluding contests with significant third-party or independent candidates. Campaign intensity may not scale linearly with spending, and the critical threshold derived from historical data may not generalize across all contexts, regions, or time periods. The authors explicitly note that the polarization spike observed in 2018 and 2020 rests on model predictions and requires further empirical validation.
Funding and Disclosures
Support came from the Austrian Science Fund (FWF) under Grants No. 10.55776/P34994 and No. EFP5 ReMASS, the Austrian Federal Ministry for Climate Action, Environment, Energy, Mobility, Innovation, and Technology under No. GZ 2023-0.841.266, and the Postdoc Program for Complexity Science and Data Competence. The provided paper text lists funding support but does not include a conflict-of-interest statement.
Publication Details
Authors: Jan Korbel, Remah Dahdoul, and Stefan Thurner, affiliated with the Complexity Science Hub, Vienna; the Section for the Science of Complex Systems, Center for Medical Data Science, Medical University of Vienna; and the Santa Fe Institute. Title: “Empirical Validation of the Polarization Transition in a Double-Random Field Model of Elections.” Published in Physical Review Letters, Volume 136, Article 127402, March 27, 2026. DOI: 10.1103/9gjj-1df6. Campaign finance data sourced from the Federal Election Commission and the Stanford Database on Ideology, Money in Politics, and Elections (DIME).







